Connected copies of data.tables

During my workflow I often make a copy of main data.frame/data.table that I do some aspects of the work on and then some other on the other copy, before joining them or something later on. However, I often experience that these copies are still connected to each other. So that edits done on one are also done on the other.Unfortunately I am not able to replicate it, but copy-pasting from my console it looks something like this: